Building band structures for long finite chains in presence of an electric field

At first, three different methods devoted to extracting the periodic-system band structures from the results of finite-system calculations are being discussed. Special emphasis is put on the performance of these methods for a system that is exposed to an external electrostatic field. Using model calculations we found that the three methods converge to the same results in the absence of the electrostatic field, but they lead to small differences when the field is included, which can be ascribed to distortions of the spatial extensions of the orbitals generated by the field. These small differences become important when addressing the issue whether it is possible to identify uniquely a set of band structures for the infinite, periodic system exposed to an electrostatic field. This question, related to the question whether the phases of the periodic-system orbitals are of physical importance, has so far not been answered. Applying the results of the first part we ultimately suggest that it is not possible to identify a unique set of band structures when the periodic system is exposed to an electrostatic field.